The point having position vectors 2i + 3j + 4k, 3i + 4j + 2k, 4i + 2j + 3k are the vertices of.

Right angled triangle

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Equilateral triangle

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Isosceles triangle

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Collinear

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Solution

The correct option is B Equilateral triangle
$\to a = 2 i + 3 j + 4 k,$
$\to b = 3 i + 4 j + 2 k,$
$\to c = 4 i + 2 j + 3 k,$
$\to a . \to b = (2 i + 3 j + 4 k) . (3 i + 4 j + 2 k)$
$= 6 + 12 + 8$
$= 26$
$\to b . \to c = (3 i + 4 j + 2 k) . (4 i + 2 j + 3 k)$
$= 12 + 8 + 6$
$= 26$
$\to c . \to a = (4 i + 2 j + 3 k) . (2 i + 3 j + 4 k)$
$= 8 + 6 + 12$
$= 26$
Hence, Since $\to a . \to b = \to b . \to c = \to c . \to a$
So it is an Equilateral triangle

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